Many have considered the question of whether Hedda Gabler can and should be considered a modern tragedy. A complete answer requires defining your two key terms: "modern" and "tragedy." Your definitions of those terms will shape your final position.
The easiest place to start, though, is with Ibsen's own position: that Ibsen considered tragedy in the personal realm to come from failure and inability to love (
That would lead you to the idea that a modern tragedy is personal, rather than a classical tragedy (which required the tragic figure to be of some marked stature).
You'd then look at how circumstances and character prevent Hedda from being able to love.
To support this, you'd look at Hedda's desires, how they are blocked by situation and society, and what the tragic results are.